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Chapter 2: Q 39. (page 79)

How many x-intercepts can the graph of a function have? How many y-intercepts can the graph of a function have?

Short Answer

Expert verified

Graph of the function has at most one y -intercept and x intercepts are none, any number or infinitely.

Step by step solution

01

Step 1. given information.

We have to check how many x and y intercepts can the graph of functions have.

02

Step 2. Concept used.

If all vertical lines intersect a curve at most once then the curve represents a function.

An x-intercept of a graph is a point where the graph crosses thex-axis.

An x-intercept occurs at a point on the graph where the y-coordinate is zero, (a,0).

A y-intercept of a graph is a point where the graph crosses the y-axis.

A y-intercept occurs at a point on the graph where the x-coordinate is zero, (0,b).

03

Step 3. Explanation.

A graph can have many intercepts, one intercept, or no intercepts.

If the graph is the graph of a function then it has at most one y-intercept,

Since the graph of a function must pass the vertical line test and they-axis is one such vertical line.

The graph of a function can have any number of x-intercepts, including none and infinitely many.

04

Step 4. Conclusion.

Hence, graph of the function has at most one y -intercept and x intercepts are none, any number or infinitely.

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Most popular questions from this chapter

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.

g(x)=x2+3x2-1

The domain of fgconsists of numbers xfor which g(x)____ 0that are in the domains of both ____ and ____.

True or False The domain of the function f(x)=x2-4xis{x|x≠±2}.

If 4,2is a point on the graph of y=f(x), which of the following points must be on the graph of y=f2(x)?

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.

h(x)=-x33x2-9
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